1.- Adjacency: Either for attacking or assisting, are creatures whose squares touch diagonally adjacent to each other?

2.- Hazardous terrain: The total effect when moving through hazardous terrain is losing 10 HP, regardless of the number of hazardous terrain squares the creature went through. Is this correct? (And yes, there is another 10 HP damage if the creature ends his movement on a hazardous terrain square).

1.- Adjacency: Either for attacking or assisting, are creatures whose squares touch diagonally adjacent to each other?

Yes.

Quote:

2.- Hazardous terrain: The total effect when moving through hazardous terrain is losing 10 HP, regardless of the number of hazardous terrain squares the creature went through. Is this correct? (And yes, there is another 10 HP damage if the creature ends his movement on a hazardous terrain square).

Pretty close.

The actual rule is that the miniature takes 10 damage for the first hazardous square it enters during *each activation*. (An activation is the entirety of one miniature's turn). Each of your miniatures in hazardous terrain then takes 10 damage at the end of your turn.

This becomes important when dealing with Forced Movement. If you force an opponent's creature into hazardous terrain, it takes 10 damage (first entering during an activation). If a different creature then forces that opponent's creature into hazardous terrain again, it'll take another 10 damage (different activation). However, it the forced movement ends with it on the Hazardous terrain, it won't take an extra 10 damage for finishing the movement there because it isn't the end of its controller's turn.